International O.R.: O.R. helps mine more ore in Chile

Using MIP models to plan extraction pays off big for world’s largest copper mining company.

By Rafael Epstein and Andrés Weintraub

copper mining in Chile

Chile produces 10 percent of the world’s copper, thanks in part to Chuquicamata, the world’s largest open pit copper mine.

Copper mining is the main export industry in Chile, and Chile is the main exporter of copper in the world. With a total annual production of two million tons, Chile accounts for 10 percent of the world’s production of copper. Several major international mining firms produce copper in Chile, including Billiton, Rio Tinto and Anglo American. The largest copper mining company in the world is CODELCO (National Copper Corporation of Chile), which, while state-owned, is run independently as a corporation.

In the last decade copper prices have risen enormously, from about $1 per pound to more than $3. CODELCO produces one-third of the $45 billion in copper that Chile exports each year, and copper accounts for 55 percent of the nation’s total exports. In 2011, CODELCO’s net revenues totaled $3 billion.

Without the income derived from CODELCO profits, it’s estimated Chile would have to raise the national value added tax from 19 percent to 22 percent to preserve the government’s current level of income. Needless to say, it’s important to Chile that the mines of CODELCO are run as efficiently as possible.

CODELCO manages seven mines; some are open pit, others are underground. In open pit mines, material is extracted from the surface, opening a large hole in a shape that looks somewhat like a stadium.
Mines contain a relatively small amount of copper. The percentage of copper, called the grade, is usually between 0.5 percent and 1.5 percent of the material extracted.

A mine is typically defined through blocks of 30x30x30 meters. For each block, the average grade of the block, its position and its volume are known. Each block is defined as “copper,” meaning it has a percentage of copper worthwhile to process, or as “sterile,” meaning it contains a percentage of copper below commercial value.

A preliminary definition of the areas to be mined is carried out through geological models, which consider the geometry of the pit and technical requirements, such as the maximum allowed slope of the pit, to ensure that the walls of the pit don’t collapse. To extract a block, all blocks situated above it must be extracted first.

The extraction process includes defining major regions to extract, called expansions or phases. In turn, each expansion is subdivided into benches, which are like steps in a staircase. They must be extracted in a logical geometric order, from top to bottom. Figures 1 and 2 show an example of the open pit operation (Epstein et al., 2012).

copper mining in Chile

Figure 1: Schematic example of benches and one expansion for an open pit.

copper mining in Chile

Figure 2: Expansions of an open pit mine, viewed from above.

Copper blocks are sent to a metallurgic process for refining, while sterile blocks are sent to waste dumps. Some blocks are sent to reserve areas when the percentage of copper is somewhat below present commercial value, under the assumption that in the future, with higher copper prices or better technology, they will be valuable.

Operations of open pit mines are similar in nature. As the open pit is excavated, roads are built in benches, which are connected to downstream processes and lead to dumps, to allow for removal of material. Rock is loosened up using explosives; cranes then load large trucks (up to 300 tons), which carry the material to designated destinations.

It is easier and cheaper to extract material from an open pit mine than an underground mine. However, when an open pit mine becomes too deep and thus impractical to operate efficiently or due to environmental constraints, the only choice is to operate an underground mine, where the ore is extracted by penetrating into the mine. Underground mines are usually divided into sectors; for each sector, engineers define the boundaries of the ore body to be extracted based on technical and economic criteria. Depending on the structure of the deposits, many different methods can be used to operate underground mines (Newman, et al., 2010). CODELCO uses block caving for its mines. In this method, the geological configuration of the deposit is expressed through blocks of 30x30x30 meters. For each block, its grade is estimated using geostatistic methods. The mine is defined through columns consisting of up to 200 vertical blocks.

The lowest block in each column is called a drawpoint. Extraction is carried out by creating a void in the drawpoint, and then the rock falls due to gravity. This process must satisfy several constraints: 1. the columns enter production in a predefined sequence given by the geometry of the mine; 2. the advance along columns must be smooth, in that all neighboring columns must have a similar height; and 3. there is a maximum rate of extraction to prevent collapse of the walls.

Thanks to gravity, the extracted rock falls through shafts and passes through several crushers to reduce its size before it is transported by train for further processing. Figure 3 shows a schematic of the process.

copper mining in Chile

Figure 3: Schematic description of the production chain for an underground mine.

Computer-based systems have been used a long time for planning the long-term extraction of open pit mines. A seminal work by Learch and Grossman (L&G) in 1965 produced a good, tractable method to determine the shape of an approximately optimal pit. Several commercial codes have been widely used based on the L&G method.

Multiple articles have shown how the L&G method can be improved. Also, methods to determine a cut-off grade have been developed, that is, the minimum grade at which it is worthwhile to extract a block (Newman et al., 2010). These methods, while proven highly useful, have limitations. For example, scheduling along time is not considered.

In an optimal extraction, there is no fixed cut-off grade; the profitability of extracting a block depends on how other blocks are handled. Institutional constraints play a role and should be considered, such as the need to satisfy contracts.

For underground mines, no easy modeling exists compared to L&G, given the multiple forms of extraction and the more complex geometry. In the last decade, the development of more powerful computers and software has allowed the introduction of mixed integer programming (MIP) to handle these problems for both types of mines.

MIP approaches have the clear advantage of overcoming the above limitations, as they can deal with time sequencing, constraints and the relation between blocks. The problem is still complex, as hundreds of thousands of 0-1 variables representing block extraction can exist. Several algorithmic approaches have been proposed, such as Branch and Cut, heuristics and aggregation of variables (Newman, et al., 2010). Newman, et al. also reports applying MIP techniques to real mines.

CODELCO strongly emphasizes using sophisticated tools to achieve efficiency. It is of interest to note that in August 2010, when 33 miners became trapped in an underground mine in Chile, the technical leader of the team that rescued them was the general manager of the underground mine El Teniente owned by CODELCO. He was also our main counterpart at CODELCO on our project with the company.
The authors started working with CODELCO in 1999. Our first project was with El Teniente, a very large underground mine. The extraction method, as described above, was block caving.

We were faced with two main decision problems:

1. At which point in time should a column start being processed? 2. A column is composed of blocks. Planners must decide how many blocks should be extracted in a column. Since the grade of blocks decreases the further up you go, at some point it is more profitable to abandon a column and start the next one. Once a column is abandoned, it can’t be worked again for safety reasons.

The problem was modeled in a network flow structure, where the nodes correspond to activities (extraction, process) and the arcs to transportation. The model we built, with a horizon of 25 years, comprised the whole production chain, from extraction in the mine to the final process to obtain commercial copper. The model addresses such decisions as when to extract, if at all, each block, the flows downstream and the volumes processed at the crushers, mills and plant.

The constraints included flow conservation, linking the sequence of extraction of columns as well as the blocks within a column, the maximum rate of extraction, the required smoothness between columns and the capacities at each process. The model had 440,000 constraints and 530,000 variables, 196,000 of which were 0-1. For the solution we had to use a heuristic approximation, solving the LP first and devising a rounding-off procedure. The fact that as the mining operation goes upward in a column the grade of the blocks decrease led to a small error in the approximation.

An evaluation of the advantage of using the model indicated that the value of the mine had increased by $100 million.

The open pit methods allowed for some aggregation, as we did not need to consider the detailed blocks but dealt directly with benches. The corresponding decision variable is 0-1 to represent if a bench is extracted, and a continuous variable to represent the tonnage extracted in each period from a bench. The constraints include how benches can be extracted to satisfy logical and geomechanical constraints, as well as the maximum rate of extraction. The model looks for an optimal net return. The LP formulation was weak; to strengthen it, we developed a multi-commodity formulation. The model had 245,000 constraints and 900,000 variables, of which 160,000 were 0-1.

Both models were solved with a commercial code.

The open pit model was used at CODELCO North Division, integrating the extraction process of two mines, Chuquicamata and RT, and their respective down-stream processes. After the model was implemented, its use was evaluated (Epstein, et al., 2012) by comparing four solutions approaches:

  1. The legacy-based model, the one used by the planners before the introduction of the new model, which considered each mine and its respective downstream processing run independently.
  2. Using the model, but keeping each mine independent.
  3. The legacy-based approach, but integrating the mines.
  4. The new model approach with the mines integrated, the approach that was implemented.

The evaluation showed that the best approach, using the model and allowing the mines to integrate their downstream process was 8 percent better than the original approach used by the planners, 3 percent better than using the model without integration and 5 percent better than integrating the mines using the legacy approach.

The advantages of the proposed approach were in terms of less investment needed in machinery and more production of copper. In addition, the model indicated a change in strategy, by showing that sulfide copper from one mine should be mostly sent to the plant near the other mine, in spite of the higher transportation cost, given lower processing costs.

At another mine, Andina, 80 kilometers north of Santiago, the model has been used since 2006 to plan a mixed operation of an open pit and an underground mine. Compared to the use of the legacy model, the new model increased net income by $180 million since its implementation.

The model has also been used to test scenarios. For example, Chuquicamata is a 100-year old mine. As the pit became too deep, the mine had to be converted into an underground one. Using the model, management realized that the very expensive conversion could be delayed two years.

The system is presently used routinely for planning purposes, as data changes over time, in terms of copper prices, costs, copper grade and interruptions due to machine failure or strikes, as well as for evaluating what-if scenarios.

Rafael Epstein and Andrés Weintraub are professors in the Department of Industrial Engineering, Universidad de Chile.

References

  1. Newman A., Rubio E., Caro R., Weintraub A., Eurek Kelly, 2010, “A Review of Operations Research in Mine Planning,” Interfaces, Vol. 40, No. 3, pp. 222-245.
  2. Esptein R., Goig M., Weintraub A., Catalán J., Santibañez P., Urrutia R., Cancino R., Gaete S., Aguayo A., Caros F., 2012, “Optimizing Long-Term Production Plans in Underground and Open Pit Cooper Mines,” Operations Research, Vol. 60, No. 1., pp. 46-70.